Tseng et al. proposed two efficient authenticated encryption schemes with message linkages for message flows. Hwang et al. (IEICE Trans. Inf. and Syst., Vol. E89-D, No. 4, April 2006) presented a forgery attack against these two schemes and proposed an improvement that they claim resists such attacks. In this paper, we show that the improved authenticated encryption schemes proposed by Hwang et al. are not secure by presenting another message forgery attack against these improved schemes.